A significantly revised and improved introduction to a critical aspect of scientific computation Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights. This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes: * Numerous examples and exercises on applications including electrical circuits, elasticity (mass-spring systems), and simple partial differential equations * Early introduction of the singular value decomposition * A new chapter on iterative methods, including the powerful preconditioned conjugate-gradient method for solving symmetric, positive definite systems * An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods With in-depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank-one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.

A significantly revised and improved introduction to a criticalaspect of scientific computationMatrix computations lie at the heart of most scientificcomputational tasks. For any scientist or engineer doinglarge-scale simulations, an understanding of the topic isessential. Fundamentals of Matrix Computations, Second Editionexplains matrix computations and the accompanying theory clearlyand in detail, along with useful insights.This Second Edition of a popular text has now been revised andimproved to appeal to the needs of practicing scientists andgraduate and advanced undergraduate students. New to this editionis the use of MATLAB for many of the exercises and examplesalthough the Fortran exercises in the First Edition have been keptfor those who want to use them. This new edition includes:* Numerous examples and exercises on applications includingelectrical circuits, elasticity (mass-spring systems), and simplepartial differential equations* Early introduction of the singular value decomposition* A new chapter on iterative methods, including the powerfulpreconditioned conjugate-gradient method for solving symmetricpositive definite systems* An introduction to new methods for solving large, sparseeigenvalue problems including the popular implicitly-restartedArnoldi and Jacobi-Davidson methodsWith in-depth discussions of such other topics as moderncomponentwise error analysis, reorthogonalization, and rank-oneupdates of the QR decomposition, Fundamentals of MatrixComputations, Second Edition will prove to be a versatile companionto novice and practicing mathematicians who seek mastery of matrixcomputation.

Preface.Acnowledgments.Gaussian Elimination and its Variants.Sensitivity of Linear Systems.The Least Squares Problem.The Singular Value Decomposition.Eigenvalues and Eigenvectors I.Eigenvalues and Eigenvectors II.Iterative Methods for Linear Systems.Appendix: Some Sources of Software for Matrix Computations.References.Index.Index of MATLAB Terms.